Mathematical Statistics with Applications
7th Edition
ISBN: 9781111798789
Author: Dennis O. Wackerly
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 4.4, Problem 54E
a.
To determine
Compute the
b.
To determine
Find the
Find the variance of the measurement errors.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
In order to find probability, you can use this formula in Microsoft Excel:
The best way to understand and solve these problems is by first drawing a bell curve and marking key points such as x, the mean, and the areas of interest. Once marked on the bell curve, figure out what calculations are needed to find the area of interest.
=NORM.DIST(x, Mean, Standard Dev., TRUE).
When the question mentions “greater than” you may have to subtract your answer from 1.
When the question mentions “between (two values)”, you need to do separate calculation for both values and then subtract their results to get the answer.
1.
Compute the probability of a value between 44.0 and 55.0.
(The question requires finding probability value between 44 and 55. Solve it in 3 steps.
In the first step, use the above formula and x = 44, calculate probability value.
In the second step repeat the first step with the only difference that x=55.
In the third step, subtract the answer of the first part from the…
If a uniform distribution is defined over the interval from 6 to 10, then answer the followings:
What is the mean of this uniform distribution?
Show that the probability of any value between 6 and 10 is equal to 1.0
Find the probability of a value more than 7.
Find the probability of a value between 7 and 9.
The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be:
More than $27?
Less than or equal to $24?
The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches.
What is the mean amount of rainfall for the month?
What is the probability of less than an inch of rain for the month?
What is the probability of exactly 1.00 inch of rain?
What is the probability of more than 1.50 inches of rain for the month?
The best way to solve this problem is begin by creating a chart. Clearly mark the range, identifying the lower and upper…
Problem 1:
The mean hourly pay of an American Airlines flight attendant is normally distributed with a mean of 40 per hour and a standard deviation of 3.00 per hour. What is the probability that the hourly pay of a randomly selected flight attendant is:
Between the mean and $45 per hour?
More than $45 per hour?
Less than $32 per hour?
Problem 2:
The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds.
What is the area between 415 pounds and the mean of 400 pounds?
What is the area between the mean and 395 pounds?
What is the probability of randomly selecting a value less than 395 pounds?
Problem 3:
In New York State, the mean salary for high school teachers in 2022 was 81,410 with a standard deviation of 9,500. Only Alaska’s mean salary was higher. Assume New York’s state salaries follow a normal distribution.
What percent of New York State high school teachers earn between 70,000 and 75,000?
What percent of New York State high school…
Chapter 4 Solutions
Mathematical Statistics with Applications
Ch. 4.2 - Prob. 1ECh. 4.2 - A box contains five keys, only one of which will...Ch. 4.2 - A Bernoulli random variable is one that assumes...Ch. 4.2 - Let Y be a binomial random variable with n = 1 and...Ch. 4.2 - Suppose that Y is a random variable that takes on...Ch. 4.2 - Consider a random variable with a geometric...Ch. 4.2 - Let Y be a binomial random variable with n=10 and...Ch. 4.2 - Prob. 8ECh. 4.2 - A random variable Y has the following distribution...Ch. 4.2 - Refer to the density function given in Exercise...
Ch. 4.2 - Suppose that Y possesses the density function...Ch. 4.2 - Prob. 12ECh. 4.2 - A supplier of kerosene has a 150-gallon tank that...Ch. 4.2 - A gas station operates two pumps, each of which...Ch. 4.2 - As a measure of intelligence, mice are timed when...Ch. 4.2 - Let Y possess a density function...Ch. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.3 - Prob. 20ECh. 4.3 - If, as in Exercise 4.17, Y has density function...Ch. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - If Y is a continuous random variable with density...Ch. 4.3 - Prob. 25ECh. 4.3 - If Y is a continuous random variable with mean ...Ch. 4.3 - Prob. 27ECh. 4.3 - Prob. 28ECh. 4.3 - Prob. 29ECh. 4.3 - The proportion of time Y that an industrial robot...Ch. 4.3 - Prob. 31ECh. 4.3 - Weekly CPU time used by an accounting firm has...Ch. 4.3 - The pH of water samples from a specific lake is a...Ch. 4.3 - Prob. 34ECh. 4.3 - If Y is a continuous random variable such that...Ch. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.4 - Suppose that Y has a uniform distribution over the...Ch. 4.4 - If a parachutist lands at a random point on a line...Ch. 4.4 - Suppose that three parachutists operate...Ch. 4.4 - Prob. 41ECh. 4.4 - Prob. 42ECh. 4.4 - A circle of radius r has area A = r2. If a random...Ch. 4.4 - Prob. 44ECh. 4.4 - Upon studying low bids for shipping contracts, a...Ch. 4.4 - 4.45 Upon studying low bids for shipping...Ch. 4.4 - The failure of a circuit board interrupts work...Ch. 4.4 - If a point is randomly located in an interval (a,...Ch. 4.4 - Prob. 49ECh. 4.4 - Prob. 50ECh. 4.4 - The cycle time for trucks hauling concrete to a...Ch. 4.4 - Refer to Exercise 4.51. Find the mean and variance...Ch. 4.4 - Prob. 53ECh. 4.4 - Prob. 54ECh. 4.4 - Refer to Exercise 4.54. Suppose that measurement...Ch. 4.4 - Refer to Example 4.7. Find the conditional...Ch. 4.4 - Prob. 57ECh. 4.5 - Use Table 4, Appendix 3, to find the following...Ch. 4.5 - Prob. 59ECh. 4.5 - Prob. 60ECh. 4.5 - What is the median of a normally distributed...Ch. 4.5 - If Z is a standard normal random variable, what is...Ch. 4.5 - A company that manufactures and bottles apple...Ch. 4.5 - The weekly amount of money spent on maintenance...Ch. 4.5 - In Exercise 4.64, how much should be budgeted for...Ch. 4.5 - A machining operation produces bearings with...Ch. 4.5 - Prob. 67ECh. 4.5 - Prob. 68ECh. 4.5 - Refer to Exercise 4.68. If students possessing a...Ch. 4.5 - Refer to Exercise 4.68. Suppose that three...Ch. 4.5 - Wires manufactured for use in a computer system...Ch. 4.5 - Prob. 72ECh. 4.5 - The width of bolts of fabric is normally...Ch. 4.5 - A soft-drink machine can be regulated so that it...Ch. 4.5 - The machine described in Exercise 4.75 has...Ch. 4.5 - The SAT and ACT college entrance exams are taken...Ch. 4.5 - Show that the maximum value of the normal density...Ch. 4.5 - Show that the normal density with parameters and ...Ch. 4.5 - Assume that Y is normally distributed with mean ...Ch. 4.6 - a If 0, () is defined by ()=0y1eydy, show that...Ch. 4.6 - Use the results obtained in Exercise 4.81 to prove...Ch. 4.6 - The magnitude of earthquakes recorded in a region...Ch. 4.6 - If Y has an exponential distribution and P(Y 2) =...Ch. 4.6 - Refer to Exercise 4.88. Of the next ten...Ch. 4.6 - The operator of a pumping station has observed...Ch. 4.6 - The length of time Y necessary to complete a key...Ch. 4.6 - Historical evidence indicates that times between...Ch. 4.6 - One-hour carbon monoxide concentrations in air...Ch. 4.6 - Prob. 95ECh. 4.6 - Prob. 96ECh. 4.6 - Prob. 97ECh. 4.6 - Consider the plant of Exercise 4.97. How much of...Ch. 4.6 - If 0 and is a positive integer, the...Ch. 4.6 - Prob. 100ECh. 4.6 - Applet Exercise Refer to Exercise 4.88. Suppose...Ch. 4.6 - Prob. 102ECh. 4.6 - Explosive devices used in mining operations...Ch. 4.6 - The lifetime (in hours) Y of an electronic...Ch. 4.6 - Four-week summer rainfall totals in a section of...Ch. 4.6 - The response times on an online computer terminal...Ch. 4.6 - Refer to Exercise 4.106. a. Use Tchebysheffs...Ch. 4.6 - The weekly amount of downtime Y (in hours) for an...Ch. 4.6 - If Y has a probability density function given by...Ch. 4.6 - Suppose that Y has a gamma distribution with...Ch. 4.6 - Prob. 112ECh. 4.7 - Prob. 120ECh. 4.7 - Prob. 122ECh. 4.7 - The relative humidity Y, when measured at a...Ch. 4.7 - The percentage of impurities per batch in a...Ch. 4.7 - Prob. 125ECh. 4.7 - Suppose that a random variable Y has a probability...Ch. 4.7 - Verify that if Y has a beta distribution with = ...Ch. 4.7 - Prob. 128ECh. 4.7 - During an eight-hour shift, the proportion of time...Ch. 4.7 - Prob. 130ECh. 4.7 - Errors in measuring the time of arrival of a wave...Ch. 4.7 - Prob. 132ECh. 4.7 - Prob. 133ECh. 4.7 - Prob. 134ECh. 4.7 - Prob. 135ECh. 4.9 - Suppose that the waiting time for the first...Ch. 4.9 - Prob. 137ECh. 4.9 - Example 4.16 derives the moment-generating...Ch. 4.9 - The moment-generating function of a normally...Ch. 4.9 - Identify the distributions of the random variables...Ch. 4.9 - If 1 2, derive the moment-generating function of...Ch. 4.9 - Refer to Exercises 4.141 and 4.137. Suppose that Y...Ch. 4.9 - The moment-generating function for the gamma...Ch. 4.9 - Consider a random variable Y with density function...Ch. 4.9 - A random variable Y has the density function...Ch. 4.10 - A manufacturer of tires wants to advertise a...Ch. 4.10 - A machine used to fill cereal boxes dispenses, on...Ch. 4.10 - Find P(|Y | 2) for Exercise 4.16. Compare with...Ch. 4.10 - Find P(|Y | 2) for the uniform random variable....Ch. 4.10 - Prob. 150ECh. 4.10 - Prob. 151ECh. 4.10 - Refer to Exercise 4.109. Find an interval that...Ch. 4.10 - Refer to Exercise 4.129. Find an interval for...Ch. 4.11 - A builder of houses needs to order some supplies...Ch. 4.11 - Prob. 157ECh. 4.11 - Consider the nail-firing device of Example 4.15....Ch. 4.11 - Prob. 159ECh. 4 - Prob. 160SECh. 4 - Prob. 161SECh. 4 - Prob. 162SECh. 4 - Prob. 163SECh. 4 - The length of life of oil-drilling bits depends...Ch. 4 - Prob. 165SECh. 4 - Prob. 166SECh. 4 - Prob. 167SECh. 4 - Prob. 168SECh. 4 - An argument similar to that of Exercise 4.168 can...Ch. 4 - Prob. 170SECh. 4 - Suppose that customers arrive at a checkout...Ch. 4 - Prob. 172SECh. 4 - Prob. 173SECh. 4 - Prob. 174SECh. 4 - Prob. 175SECh. 4 - If Y has an exponential distribution with mean ,...Ch. 4 - Prob. 180SECh. 4 - Prob. 181SECh. 4 - Prob. 182SECh. 4 - Prob. 183SECh. 4 - Prob. 184SECh. 4 - Prob. 185SECh. 4 - Prob. 186SECh. 4 - Refer to Exercise 4.186. Resistors used in the...Ch. 4 - Prob. 188SECh. 4 - Prob. 189SECh. 4 - Prob. 190SECh. 4 - Prob. 191SECh. 4 - The velocities of gas particles can be modeled by...Ch. 4 - Because P(YyYc)=F(y)F(c)1F(c) has the properties...Ch. 4 - Prob. 194SECh. 4 - Prob. 195SECh. 4 - Prob. 196SECh. 4 - Prob. 197SECh. 4 - Prob. 198SECh. 4 - Prob. 199SECh. 4 - Prob. 200SE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- Pls help asaparrow_forwardSolve the following LP problem using the Extreme Point Theorem: Subject to: Maximize Z-6+4y 2+y≤8 2x + y ≤10 2,y20 Solve it using the graphical method. Guidelines for preparation for the teacher's questions: Understand the basics of Linear Programming (LP) 1. Know how to formulate an LP model. 2. Be able to identify decision variables, objective functions, and constraints. Be comfortable with graphical solutions 3. Know how to plot feasible regions and find extreme points. 4. Understand how constraints affect the solution space. Understand the Extreme Point Theorem 5. Know why solutions always occur at extreme points. 6. Be able to explain how optimization changes with different constraints. Think about real-world implications 7. Consider how removing or modifying constraints affects the solution. 8. Be prepared to explain why LP problems are used in business, economics, and operations research.arrow_forwardged the variance for group 1) Different groups of male stalk-eyed flies were raised on different diets: a high nutrient corn diet vs. a low nutrient cotton wool diet. Investigators wanted to see if diet quality influenced eye-stalk length. They obtained the following data: d Diet Sample Mean Eye-stalk Length Variance in Eye-stalk d size, n (mm) Length (mm²) Corn (group 1) 21 2.05 0.0558 Cotton (group 2) 24 1.54 0.0812 =205-1.54-05T a) Construct a 95% confidence interval for the difference in mean eye-stalk length between the two diets (e.g., use group 1 - group 2).arrow_forward
- An article in Business Week discussed the large spread between the federal funds rate and the average credit card rate. The table below is a frequency distribution of the credit card rate charged by the top 100 issuers. Credit Card Rates Credit Card Rate Frequency 18% -23% 19 17% -17.9% 16 16% -16.9% 31 15% -15.9% 26 14% -14.9% Copy Data 8 Step 1 of 2: Calculate the average credit card rate charged by the top 100 issuers based on the frequency distribution. Round your answer to two decimal places.arrow_forwardPlease could you check my answersarrow_forwardLet Y₁, Y2,, Yy be random variables from an Exponential distribution with unknown mean 0. Let Ô be the maximum likelihood estimates for 0. The probability density function of y; is given by P(Yi; 0) = 0, yi≥ 0. The maximum likelihood estimate is given as follows: Select one: = n Σ19 1 Σ19 n-1 Σ19: n² Σ1arrow_forward
- Please could you help me answer parts d and e. Thanksarrow_forwardWhen fitting the model E[Y] = Bo+B1x1,i + B2x2; to a set of n = 25 observations, the following results were obtained using the general linear model notation: and 25 219 10232 551 XTX = 219 10232 3055 133899 133899 6725688, XTY 7361 337051 (XX)-- 0.1132 -0.0044 -0.00008 -0.0044 0.0027 -0.00004 -0.00008 -0.00004 0.00000129, Construct a multiple linear regression model Yin terms of the explanatory variables 1,i, x2,i- a) What is the value of the least squares estimate of the regression coefficient for 1,+? Give your answer correct to 3 decimal places. B1 b) Given that SSR = 5550, and SST=5784. Calculate the value of the MSg correct to 2 decimal places. c) What is the F statistics for this model correct to 2 decimal places?arrow_forwardCalculate the sample mean and sample variance for the following frequency distribution of heart rates for a sample of American adults. If necessary, round to one more decimal place than the largest number of decimal places given in the data. Heart Rates in Beats per Minute Class Frequency 51-58 5 59-66 8 67-74 9 75-82 7 83-90 8arrow_forward
- can someone solvearrow_forwardQUAT6221wA1 Accessibility Mode Immersiv Q.1.2 Match the definition in column X with the correct term in column Y. Two marks will be awarded for each correct answer. (20) COLUMN X Q.1.2.1 COLUMN Y Condenses sample data into a few summary A. Statistics measures Q.1.2.2 The collection of all possible observations that exist for the random variable under study. B. Descriptive statistics Q.1.2.3 Describes a characteristic of a sample. C. Ordinal-scaled data Q.1.2.4 The actual values or outcomes are recorded on a random variable. D. Inferential statistics 0.1.2.5 Categorical data, where the categories have an implied ranking. E. Data Q.1.2.6 A set of mathematically based tools & techniques that transform raw data into F. Statistical modelling information to support effective decision- making. 45 Q Search 28 # 00 8 LO 1 f F10 Prise 11+arrow_forwardStudents - Term 1 - Def X W QUAT6221wA1.docx X C Chat - Learn with Chegg | Cheg X | + w:/r/sites/TertiaryStudents/_layouts/15/Doc.aspx?sourcedoc=%7B2759DFAB-EA5E-4526-9991-9087A973B894% QUAT6221wA1 Accessibility Mode பg Immer The following table indicates the unit prices (in Rands) and quantities of three consumer products to be held in a supermarket warehouse in Lenasia over the time period from April to July 2025. APRIL 2025 JULY 2025 PRODUCT Unit Price (po) Quantity (q0)) Unit Price (p₁) Quantity (q1) Mineral Water R23.70 403 R25.70 423 H&S Shampoo R77.00 922 R79.40 899 Toilet Paper R106.50 725 R104.70 730 The Independent Institute of Education (Pty) Ltd 2025 Q Search L W f Page 7 of 9arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
Statistics 4.1 Point Estimators; Author: Dr. Jack L. Jackson II;https://www.youtube.com/watch?v=2MrI0J8XCEE;License: Standard YouTube License, CC-BY
Statistics 101: Point Estimators; Author: Brandon Foltz;https://www.youtube.com/watch?v=4v41z3HwLaM;License: Standard YouTube License, CC-BY
Central limit theorem; Author: 365 Data Science;https://www.youtube.com/watch?v=b5xQmk9veZ4;License: Standard YouTube License, CC-BY
Point Estimate Definition & Example; Author: Prof. Essa;https://www.youtube.com/watch?v=OTVwtvQmSn0;License: Standard Youtube License
Point Estimation; Author: Vamsidhar Ambatipudi;https://www.youtube.com/watch?v=flqhlM2bZWc;License: Standard Youtube License